Advanced Methods and Tools for ECG Data Analysis - Part 4 ppsx

P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 4.2 RR Interval Models 105 Figure 4.1 Schematic digram of the cardiovascular system following DeBoer [5]. Dashed lines in- dicate slow sympathetic control, and solid lines indicate faster parasympathetic control. The respiratory signal that drives the high-frequency variations in the model is assumed to be unaffected by the other system parameters. DeBoer chose the respi- ratory signal to be a simple sinusoid, although other investigations have explored the use of more realistic signals [20]. DeBoer’s model was the first to allow for the discrete (beat-to-beat) nature of the heart, whereas all previous models had used continuous differential equations to describe the cardiovascular system. The model consists of a set of difference equations involving systolic blood pressure (S), dias- tolic pressure (D), pulse pressure (P = S −D), peripheral resistance (R), RR interval (I), and an arterial time constant (T = RC), with C as the arterial compliance. The equations are then based upon four distinct mechanisms: 1. Control of the HR and peripheral resistance by the baroreflex: The current RR interval value, is a linear weighted combination of the last seven systolic BP values (a 0 S n a 6 S n−6 ). The current systolic value, S n , represents the vagal effect weighted by coefficient a 0 (fast with short delays), whereas S n−2 S n−6 represent sympathetic contributions (slower with longer delays). The previ- ous systolic value, S n−1 , does not contribute (a 1 = 0) because its vagal effect has already died out and the sympathetic effect is not yet active. 2. Windkessel properties of the systemic arterial tree: This represents the sym- pathetic action of the baroreflex on the peripheral resistance. The Windkessel equation, D n = c 3 S n−1 exp(−I n−1 /T n−1 ), describes the diastolic pressure P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 106 Models for ECG and RR Interval Processes decay, governed by the ratio of the previous RR interval to the previous arterial time constant. The time constant of the decay, T n , and thus (assum- ing a constant arterial compliance C) the current value of the peripheral resistance, R n , depends on a weighted sum of the previous six values of S. 3. Contractile properties of the myocardium: The influence of the length of the previous interval on the strength of the ventricular contraction is given by P n = γ I n−1 +c 2 , where γ and c 2 are physiological constants. A longer pulse interval (I n−1 > I n−2 ) therefore tends to increase the next pulse pressure (if γ>0), P n , a phenomenon motivated by the increased filling of the ven- tricles after a long interval, leading to a more forceful contraction (Starling’s law) and by the restitution properties of the myocardium (which also leads to an increased strength of contraction after a longer interval). 4. Mechanical effects of respiration on BP: Respiration is simulated by disturb- ing P n with a sinusoidal variation in I. Without this addition, the equations themselves do not imply any fluctuations in BP or HR but lead to stable values for the different variables. Linearization of the equations of motion around operating points (normal hu- man values for S, D, I, and T) was employed to facilitate an analysis of the model. Note that such a linearization is a good approximation when the subject is at rest. The addition of a simulated respiratory signal was shown to provide a good cor- respondence between the power spectra of real and simulated data. DeBoer also pointed out the need to perform cross-spectral analysis between the RR tachogram, the systolic BP, and respiration signals. Pitzalis et al. [21] performed such an analy- sis supporting DeBoer’s model and showed that the respiratory rate modulates the interrelationship between the RR interval and S variabilities: the higher the rate of respiration, the smaller the gain and the smaller the phase difference between the two. Furthermore, the same response is found after administering a β-adrenoceptor blockade, suggesting that the sympathetic drive is not involved in this process. Sleight and Casadei [7] also present evidence to support the assumptions underly- ing the DeBoer model. 4.2.3 The Research Cardiovascular Simulator The Research CardioVascular SIMulator (RCVSIM) [22–24] software 3 was devel- oped in order to complement the experimental data sets provided by PhysioBank. The human cardiovascular model underlying RCVSIM is based upon an electrical circuit analog, with charge representing blood volume (Q, ml), current representing blood flow rate ( ˙q, ml/s), voltage representing pressure (P, mmHg), capacitance rep- resenting arterial/vascular compliance (C), and resistance (R) representing frictional resistance to viscous blood flow. RCVSIM includes three major components. The first component (illustrated in Figure 4.2) is a lumped parameter model of the pulsatile heart and circulation which itself consists of six compartments, the left ventricles, the right ventricles, the systemic arteries, the systemic veins, the 3. Open-source code and further details are available from http://www.physionet.org/physiotools/rcvsim/. P1: Shashi August 24, 2006 16:0 Chan-Horizon Azuaje˙Book 4.2 RR Interval Models 107 Figure 4.2 PhysioNet’s RCVSIM lumped parameter model of the human heart-lung unit in terms of its electrical circuit analog. Charge is analogous to blood volume (Q, ml), current, to blood flow rate (˙q, ml/s), and voltage, to pressure (P , mmHg). The model consists of six compartments which represent the left and right ventricles (l,r ), systemic arteries and veins (a, v), and pulmonary arteries and veins (pa, pv). Each compartment consists of a conduit for viscous blood flow with resistance (R), a volume storage element with compliance (C ) and unstressed volume (Q 0 ). The node labeled P ”ra” (t) is the location of where the right atrium would be if it were explicitly included in the model. (Adapted from: [22] with permission. c  2006 R. Mukkamala.) pulmonary arteries, and the pulmonary veins. Each compartment consists of a con- duit for viscous blood flow with resistance (R), a volume storage element with compliance (C) and unstressed volume (Q 0 ). The second major component of the model is a short-term regulatory system based upon the DeBoer model and includes an arterial baroreflex system, a cardiopulmonary baroreflex system, and a direct neural coupling mechanism between respiration and heart rate. The third major component of RCVSIM is a model of resting physiologic perturbations which in- cludes respiration, autoregulation of local vascular beds (exogenous disturbance to systemic arterial resistance), and higher brain center activity affecting the autonomic nervous system (1/ f exogenous disturbance to heart rate [25]). The model is capable of generating realistically human pulsatile hemodynamic waveforms, cardiac function and venous return curves, and beat-to-beat hemody- namic variability. RCVSIM has been previously employed in cardiovascularresearch P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 108 Models for ECG and RR Interval Processes by its author for the development and evaluation of system identification methods aimed at the dynamical characterization of autonomic regulatory mechanisms [23]. Recent developments of RCVSIM have involved the development of a parallelized version and extensions for adaptation to space-flight data to describe the processes involved in orthostatic hypotension [26–28]. Simulink versions have been developed both with and without the baroreflex reflex mechanism, and an additional intersti- tial compartment to aid work fitting the model parameters to real data representing an instance of hemorrhagic shock [29]. These recent innovations are currently be- ing redeveloped into a platform-independent version which will shortly be available from PhysioNet [22, 30]. 4.2.4 Integral Pulse Frequency Modulation Model The integral pulse frequency modulation (IPFM) model was developed for investi- gating the generation of a discrete series of events, such as a series of heartbeats [31]. This model assumes the existence of a continuous-time input modulation signal which possesses a particular physiological interpretation, such as describing the mechanisms underlying the autonomic nervous system [32]. The action of this mod- ulation signal when integrated through the model generates a series of interbeat time intervals, which may be compared to RR intervals recorded from human subjects. The IPFM model assumes that the autonomic activity, including both the sym- pathetic and parasympathetic influences, may be represented by a single modulating input signal x(t). This input signal x(t) is integrated until a threshold, R, is reached where a beat is generated. At this point, the integrator is reset to zero and the process is repeated [31, 33] (see Figure 4.3). The beat-to-beat time series may be expressed as a series of pulses, p(t) = n =  t n 0 1 + x(t) T dt, (4.3) where n is an integer number representing the nth beat and t n reflects its time stamp. The time T is the mean interbeat interval and x(t)/ T is the zero-mean modulating term. It is usual to assume that this modulation term is relatively small (x(t) << 1) Figure 4.3 The integral pulse frequency modulation model. The input signal x(t) is integrated yielding y(t). When y(t) reaches the fixed reference value R, a pulse is emitted and the integrator is reset to 0, whereupon the cycle starts again. Output of the model is the series of pulses p(t). When used to model the cardiac pacemaker, the input is a signal proportional to the accelerating autonomic efferences on the pacemaker cells and the output is the RR interval time series. P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 4.2 RR Interval Models 109 in order to reflect that heart rate variability is usually smaller than the mean heart rate. The time-dependent value of (1 +x(t))/T may be viewed as the instantaneous heart rate. For simplification, the first beat is assumed to occur at time t 0 = 0. Generally, x(t) is assumed to be band-limited with negligible power for frequencies greater than 0.4 Hz. In physiological terms, the output signal of the integrator can be viewed as the charging of the membrane potential of a sino-atrial pacemaker cell [34]. The potential increases until a certain threshold (R in Figure 4.3) is exceeded and then triggers an action potential which, when combined with the effect of many other action potentials, initiates another cardiac cycle. Given that the assumptions underlying the IPFM are valid, the aim is to con- struct a method for obtaining information about the input signal x(t) using the observed sequence of event times t n . The various issues concerning a reasonable choice of time domain signal for representing the activity in the heart are discussed in [32]. The IPFM model has been extended to provide a time-varying threshold inte- gral pulse frequency modulation (TVTIPFM) model [35]. This approach has been applied to RR intervals in order to discriminate between autonomic nervous mod- ulation and the mechanical stretch induced effect caused by changes in the venous return and respiratory modulation. 4.2.5 Nonlinear Deterministic Models A chaotic dynamic system may be capable of generating a wide range of irregular time series that would normally be associated with stochastic dynamics. The task of identifying whether a particular set of observations may have arisen from a chaotic system has given rise to a large body of research (see [36] and references therein). The method of surrogate data is particularly useful for constructing hypothesis tests for asking whether or not a given data set may have underlying nonlinear dynamics [37]. Nonlinear deterministic models come in a variety of forms ranging from local linear models [38–40] to radial basis functions and neural networks [41, 42]. The first step when constructing a model using nonlinear time series analysis techniques is to identify a suitable state space reconstruction. For a time series s n ,(n = 1, 2, , N), a delay coordinate reconstruction is obtained using x n =  s n−(m−1)τ , , s n−2τ , s n  (4.4) where m and τ are known as the reconstruction dimension and delay, respectively. The ability to accurately evaluate a particular reconstruction and compare various models requires an incorporation of the measurement uncertainty inherent in the data. McSharry and Smith give examples of how these techniques may be employed when analysing three different experimental datasets [43]. In particular, this inves- tigation presents a consistency check that may be used to identify why and where a particular model is inadequate and suggests a means of resolving these problems. Cao and Mees [44] developed a deterministic local linear model for analyzing nonlinear interactions between heart rate, respiration, and the oxygen saturation (SaO 2 ) wave in the cardiovascular system. This model was constructed using P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 110 Models for ECG and RR Interval Processes multichannel physiological signals from dataset B of the Santa Fe Time Series Com- petition [45]. They found that it was possible to construct a model that provides accurate forecasts of the next time step (next beat) in one signal using a combina- tion of previous values selected from the other two signals. This demonstrates that heart rate, respiration, and oxygen saturation are three key interacting factors in the cardiorespiratory cycle since no other signal is required to provide accurate pre- dictions. The investigation was repeated and it found similar results for different segments of the three signals. It should be emphasized, however, that this analy- sis was performed on only one subject who suffered from sleep apnea. In this case, a strong correlation between respiration and the cardiovascular effort is to be expected. For this reason, these results cannot be assumed to hold for normal subjects and the results may indeed be specific to only the Santa Fe Time Series. The question of whether parameters derived in specific situations are sufficiently distinct such that they can be used to identify improving or worsening conditions remains unanswered. A more detailed description of nonlinear techniques and their application to filtering ECG signals can be found in Chapter 6. 4.2.6 Coupled Oscillators and Phase Synchronization Observations of the phase differences between oscillations in HR, BP, and respira- tion have shown that, although the phases drift in a highly nonstationary manner, at certain times, phase locking can occur [3, 46, 47]. These observations led Rosen- blum et al. [48–51] to propose the idea of representing the cardiovascular system as a set of coupled oscillators, demonstrating that phase and frequency locking are not equivalent. In the presence of noise, the relative phase performs a biased ran- dom walk, resulting in no frequency locking, while retaining the presence of phase locking. Bra ˇ ci ˇ c et al. [47, 52, 53] then extended this model, consisting of five linearly coupled oscillators, ˙x i =−x i q i − ω i y i + g x i (x) ˙y i =−y i q i + ω i x i + g y i (y), q i = α i   x 2 i + y 2 i − a i  (4.5) where x, y are state vectors, g x i (x) and g y i (y) are linear coupling vectors, and α i , a i , ω i are constants governing the individual oscillators. For each oscillator i, the dynamics are described by the blood flow, x i , and the blood flow rate, y i . Numerical simulation of this model generated signals which appeared similar to the observed signals recorded from human subjects. This model with linear cou- plings and added noise is capable of displaying similar forms of synchronization as that observed for real signals. In particular, short episodes of synchronization appear and disappear at random intervals as has been observed for human subjects. One condition in which cardiorespiratory coupling is frequently observed is a type of sleep known as noncyclic alternating phase (NCAP) sleep (see Chapter 3). In fact, the changes in cardiovascular parameters over the sleep cycle and between wakefullness and sleep are an active current research field which is only just being explored (see [54–62]). In particular, Peng et al. [25, 57] have shown that the RR P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 4.2 RR Interval Models 111 interval exhibits some interesting long-range (circadian) scaling characteristics over the 24-hour period (see Section 4.2.7). Since heart rate and HRV are known to be correlated with activity and sleep [56], Lo et al. [62] later followed up this work to show that the distribution of durations of wakefullness and sleep followed different distributions; sleep episode durations follow a scale-free power law independent of species, and sleep episode durations follow an exponential law with a characteristic time scale related to body mass and metabolic rate. 4.2.7 Scale Invariance Many complex biological systems display scale-invariant properties and the absence of a characteristic scale (time and/or spatial domains) may suggest certain advan- tages in terms of the ability to easily adapt to changes caused by external sources. The traditional analysis of heart rate variability focuses on short time oscillations related to respiration (approximately between 0.15 and 0.4 Hz) and the influence of BP control mechanisms at approximately 0.1 Hz. The resting heartbeat of a healthy human tends to vary in an erratic manner and casts doubt on the homeostatic view- point of cardiovascular regulation in healthy humans. In fact, the analysis of a long time series of heartbeat interval time series (typically over 24 hours) gives rise to a1/ f -like spectrum for frequencies less than 0.1 Hz, suggesting the possibility of scale-invariance in HRV [63]. The analysis of longrecords of RR intervals, with 24 hours giving approximately 10 5 data points, is possible using ambulatory (Holter) monitors. Peng et al. [25] found that in the case of healthy subjects, these RR intervals display scale-invariant, long-range anticorrelations up to 10 4 heartbeats. The histogram of increments of the RR intervals may be described by a L ´ evy stable distribution. 4 Furthermore, a group of subjects with severe heart disease had similar distributions but the long-range correlations vanished. This suggests that the different scaling behavior in health and disease must be related to the underlying dynamics of the cardiovascular system. A log-log plot of the power spectra, S( f ), of the RR intervals displays a linear relationship, such that S( f ) ∼ f β . The value ofβ can be used to distinguish between: (1) β = 0, an uncorrelated time series also known as “white noise”; (2) −1 <β<0, correlated such that positive values are likely to be close in time to each other and the same is true for negative values; and (3) 0 <β<1, anticorrelated time series such that positive and negative values are more likely to alternate in time. The 1/f noise, β = 1, often called “pink noise,” typically displayed by cardiac interbeat intervals is an intermediate compromise between the randomness of white noise, β = 0, and the much smoother Brownian motion, β = 2. Although RR intervals from healthy subjects follow approximately β ∼ 1, RR intervals from heart failure subjects have β ∼ 1.6, which is closer to Brownian motion [65]. This variation in scaling suggests that the value of β may provide the basis of a usefulmedical diagnostic. While there are a number of techniques available 4. A heavy-tailed generalization of the normal distribution [64]. P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 112 Models for ECG and RR Interval Processes for quantifying self-similarity, detrended fluctuation analysis is often employed to measure the self-similarity of nonstationary biomedical signals [66]. DFA provides a scaling coefficient, α, which is related to β via β = 2α − 1. McSharry and Malamud [67] compared five different techniques for quanti- fying self-similarity in time series; these included power-spectral, wavelet variance, semivariograms, rescaled-range, and detrended fluctuation analysis. Each technique was applied to both normal and log-normal synthetic fractional noises and motions generated using a spectral method, where a normally distributed white noise was appropriately filtered such that its power-spectral density, S, varied with frequency, f , according to S ∼ f −β . The five techniques provide varying levels of accuracy depending on β and the degree of nonnormality of the time series being considered. For normally distributed time series, semivariograms provide accurate estimates for 1.2 <β<2.5, rescaled range for 0.0 <β<0.8, DFA for −0.8 <β<2.2, and power spectra and wavelets for all values of β. All techniques demonstrate decreasing accuracy for log-normal fractional noises with increasing coefficient of variance, particularly for antipersistent time series. Wavelet analysis offers the best performance both in terms of providing accurate estimates for normally distributed time series over the entire range −2 ≤ β ≤ 4 and having the least decrease in accuracy for log-normal noises. The existence of a power law spectrum provides a necessary condition for scale invariance in the process underlying heart rate variability. Ivanov et al. [68] demon- strated that the normal healthy human heartbeat, even under resting conditions, fluctuates in a complex manner and has a multifractal 5 temporal structure. Fur- thermore, there was evidence of a loss of multifractality (to monofractality) in cases of congestive heart failure. Scaling techniques adapted from statistical physics have revealed the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales (see [65, 68] and references therein). A number of different statistical models have been proposed to explain the mechanisms underlying the heart rate variability of healthy human subjects. Lin and Hughson [69] present a model motivated by an analogy with turbulence. This approach provides a cascade-type multifractal model for determining the defor- mation of the distribution of RR intervals. One feature of such a model is that of evolving from a Gaussian distribution at small scales to a stretched exponen- tial at smaller scales. Kiyono et al. [70] argue that the healthy human heart rate is controlled to converge continually to a critical state and show that their model is capable of providing a better fit to the observed data than that of the random (multiplicative) cascade model reported in [69]. Kuusela et al. [71] present a model based on a simple one-dimensional Langevin-type stochastic difference equation, which can describe the fluctuations in the heart rate. This model is capable of ex- plaining the multifractal behavior seen in real data and suggests how pathologic cases simplify the heart rate control system. 5. Monofractal signals are homogeneous in that only one scaling exponent is needed to describe all segments of the signal. In contrast, multifractal signals requires a range of different exponents to explain their scaling properties. P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 4.2 RR Interval Models 113 4.2.8 PhysioNet Challenge The PhysioNet challenge of 2002 6 invited participants to design a numerical model for generating 24-hour records of RR intervals. A second part of the challenge asked participants to use their respective signal processing techniques to identify the real and artificial records from among a database of unmarked 24-hour RR tachograms. The wide range of models entered for the competition reflects the nu- merous approaches available for investigating heart rate variability. The following paragraphs summarize these approaches, which include a multiplicative cascade model, a Markovian model, and a heuristic multiscale approach based on empirical observations. Lin and Hughson [69] explored the multifractal HRV displayed in healthy and other physiological conditions, including autonomic blockades and congestive heart failure, by using a multiplicative random cascade model. Their method used a bounded cascade model to generate artificial time series which was able to mimic some of the known phenomenology of HRV in healthy humans: (1) multifractal spectrum including 1/ f power law, (2) the transition from stretch-exponential to Gaussian probability density function in the interbeat interval increment data and (3) the Poisson excursion law in small RR increments [72]. The cascade consisted of a discrete fragmentation process and assigned random weights to the cascade components of the fragmented time intervals. The artificial time series was finally constructed by multiplying the cascade components in each level. Yang et al. [73] employed symbolic dynamics and probabilistic automaton to construct a Markovian model for characterizing the complex dynamics of healthy human heart rate signals. Their approach was to simplify the dynamics by mapping the output to binary sequences, where the increase and decrease of the interbeat interval were denoted by 1 and 0, respectively. In this way, it was also possible to define a m-bit symbolic sequence to characterize transitions of symbolic dynamics. For the simplest model consisting of 2-bit sequences, there are four possible sym- bolic sequences including 11, 10, 00, and 01. Moreover, each symbolic sequence has two possible transitions, for example, 1(0) can be transformed to (0)0, which results in decreasing RR intervals, or (0)1 and vice versa. In order to define the mechanism underlying these symbolic transitions, the authors utilized the concept of probabilistic automaton in which the transition from current symbolic sequence to next state takes place with a certain probability in a given range of RR intervals. The model used 8-bit sequences and a probability table obtained from the RR time series of healthy humans from Taipei Veterans General Hospital and PhysioNet. The resulting generator is comprised of the following major components: (1) the symbolic sequence as a state of RR dynamics, (2) the probability table defining transitions between two sequences, and (3) an absolute Gaussian noise process for governing increments of RR intervals. McSharry et al. [74] used a heuristic empirical approach for modeling the fluctuations of the beat-to-beat RR intervals of a normal healthy human over 24 hours by considering the different time scales independently. Short range vari- ability due to Mayer waves and RSA were incorporated into the algorithm using a 6. See http://www.physionet.org/challenge/2002 for more details. P1: Shashi August 24, 2006 11:42 Chan-Horizon Azuaje˙Book 114 Models for ECG and RR Interval Processes power spectrum with given spectral characteristics described by its low frequency and high frequency components, respectively [75]. Longer range fluctuations aris- ing from transitions between physiological states were generated using switching distributions extracted from real data. The model generated realistic synthetic 24- hour RR tachograms by including both cardiovascular interactions and transitions between physiological states. The algorithm included the effects of various physi- ological states, including sleep states, using RR intervals with specific means and trends. An analysis of ectopic beat and artifact incidence in an accompanying pa- per [76] was usedto provide a mechanism for generating realistic ectopy and artifact. Ectopic beats were added with an independent probability of one per hour. Artifacts were included with a probability proportional to mean heart rate within a state and increased for state transition periods. The algorithm provides RR tachograms that are similar to those in the MIT-BIH Normal Sinus Rhythm Database. 4.2.9 RR Interval Models for Abnormal Rhythms Chapter 1 described some of the mechanisms that activate and mediate arrhythmias of the heart. Broadly speaking, modeling of arrhythmias can be broken down into two subgroups: ventricular arrhythmias and atrial arrhythmias. The models tend to describe either the underlying RR interval processes or the manifest waveform (ECG). Furthermore, the models are formulated either from the cellular conduction perspective (usually for RR interval models) or from an empirical standpoint. Since the connection between the underlying beat-to-beat interval process and the resul- tant waveform is complex, empirical models of the ECG waveform are common. These include simple time domain templates [77], Fourier and AR models [78], singular value decomposition-based techniques [79, 80], and more complex meth- ods such as neural network classifiers [81–83], and finite element models [84]. Such models are usually applied on a beat-by-beat basis. Furthermore, due to the fact that the classifiers are trained using a cost function based upon a distance metric between waveforms, small deviations in the waveform morphology (such as that seen in atrial arrhythmias) are often poorly identified. In the case of atrial arrhythmias, unless a full three-dimensional model of the cardiac potentials is used (such as in Cherry et al. [85]), it is often more appropriate to analyze the RR interval process itself. The following gives a chronological summary of the developments in modeling atrial fibrillation. In 1983, Cohen et al. [86] introduced a model for the ventricular response during AF that treated the atrio-ventricular junction as a lumped parameter structure with defined electrical properties such as the refactory period and period of autorhymicity, that is being continually bombarded by random AF impulses. Although this model could account for all the principal statistical properties of the RR interval distribution during AF, several important physiological properties of the heart were not included in the model (such as conduction delays within the AV junction and ventricle and the effect of ventricular pacing). In 1988, Wittkampf et al. [87–89] explained the fact that short RR intervals during AF could be eliminated by ventricular pacing at relatively long cycle lengths through a model that modulates the AV node pacemaker rate and rhythm by AF impulses. However, this model failed to explain the relationship between most of the captured beats and the shortest RR interval length in a canine model. [...]... Chan-Horizon 4. 4 Conclusion [32] [33] [ 34] [35] [36] [37] [38] [39] [40 ] [41 ] [42 ] [43 ] [44 ] [45 ] [46 ] [47 ] [48 ] [49 ] [50] [51] Azuaje˙Book 129 Mateo, J., and P Laguna, “Improved Heart Rate Variability Signal Analysis from the Beat Occurrence Times According to the IPFM Model,” IEEE Trans Biomed Eng., Vol 47 , No 8, 2000, pp 985–996 Rompelman, O., J D Snijders, and C van Spronsen, “The Measurement of... realistic ECG signals with complete flexibility over the choice of parameters that govern the structure of these ECG signals in both the temporal and spectral domains The model also allows the average morphology of the ECG P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 118 Models for ECG and RR Interval Processes Figure 4. 4 ECGSYN flow chart describing the procedure for specifying the temporal and. .. rate mean Heart rate standard deviation Low frequency High frequency Low-frequency standard deviation High-frequency standard deviation LF/HF ratio Notation N fecg fint A hmean hstd f1 f2 c1 c2 γ Defaults 256 256 Hz 512 Hz 0.1 mV 60 bpm 1 bpm 0.1 Hz 0.25 Hz 0.1 Hz 0.1 Hz 0.5 P1: Shashi August 24, 2006 11 :42 Chan-Horizon 4. 3 ECG Models Azuaje˙Book 123 Figure 4. 8 Synthetic ECG signals for different mean... this part of the model could be made more realistic by coupling the baseline wander to a phase-lagged signal derived from highpass filtering (fc = 0.15 Hz) the RR P1: Shashi August 24, 2006 1 24 11 :42 Chan-Horizon Azuaje˙Book Models for ECG and RR Interval Processes interval time series The phase lag is important, since RSA and mechanical effects on the ECG and RR time series are not in phase (and often... with realistic coupling to the ECG The model has also been use to generate a 12-lead simulator for training in coronary artery disease identification as part of American Board of Family Practice Maintenance of P1: Shashi August 24, 2006 11 :42 Chan-Horizon 126 Azuaje˙Book Models for ECG and RR Interval Processes Figure 4. 10 Example of a 12-lead version of ECGSYN, produced for [120] by Dr Guy Roussel of... Lian et al [ 94] for further details and experimental results) 4. 3 ECG Models The following sections show two disparate approaches to modeling the ECG While both paradigms can produce an ECG signal and are consistent with various aspects of the physiology, they attempt to replicate different observed phenomena on P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 116 Models for ECG and RR Interval... Ruha, A., and S Nissila, “A Real-Time Microprocessor QRS Detector System with a 1-ms Timing Accuracy for the Measurement of Ambulatory HRV,” IEEE Trans Biomed Eng., Vol 44 , No 3, 1997, pp 159–167 Laguna, P., G B Moody, and R G Mark, “Power Spectral Density of Unevenly Sampled Data by Least-Square Analysis: Performance and Application to Heart Rate Signals,” IEEE Trans Biomed Eng, Vol BME -4 5 , 1998,... Computers in Cardiology, Vol 22, September 1995, pp 46 1 46 3 Healey, J., et al., “An Open-Source Method for Simulating Atrial Fibrillation Using ECGSYN,” Computers in Cardiology, Vol 31, No 19–22, September 20 04, pp 42 5– 42 8 Clifford, G D., and P E McSharry, “A Realistic Coupled Nonlinear Artificial ECG, BP, and Respiratory Signal Generator for Assessing Noise Performance of Biomedical Signal Processing Algorithms,”... [ 74] and Section 4. 2.8) ECGSYN can be employed to generate ECG signals with known spectral characteristics and can be used to test the effect of varying the ECG sampling frequency fecg on the estimation of HRV metrics In the following analysis, estimates of the LF/HF ratio were calculated for a range of sampling frequencies (Figure 4. 9) ECGSYN was operated using a mean heart rate of 60 bpm, a standard... indicated Figure 4. 7 Three-dimensional state space of the dynamical system given by integrating (4. 10) showing motion around the limit cycle in the horizontal (x, y)-plane The vertical z-component provides the synthetic ECG signal with a morphology that is defined by the five extrema P, Q, R, S, and T P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 4. 3 ECG Models 121 to force the trajectory . available 4. A heavy-tailed generalization of the normal distribution [ 64] . P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 112 Models for ECG and RR Interval Processes for quantifying self-similarity,. http://www.physionet.org/physiotools/ecgsyn/. P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 4. 3 ECG Models 119 Figure 4. 5 Spectral characteristics of (4. 9), the RR interval generator for ECGSYN. two. Hz Low-frequency standard deviation c 1 0.1 Hz High-frequency standard deviation c 2 0.1 Hz LF/HF ratio γ 0.5 P1: Shashi August 24, 2006 11 :42 Chan-Horizon Azuaje˙Book 4. 3 ECG Models 123 Figure 4. 8